Are small(ish) internal fractures at seams of drywall something to be concerned about?

Question

I'm framing a door and putting up new drywall, and I was wondering whether small internal cracks at the seams are an issue. I'm not sure if I'm referring to them correctly, if not let me know.

For example, this is just a 2ftx2in strip, and I'll probably just replace it, as it wouldn't be difficult.

But this is large panel that got damaged when I ripped out the old door header, and it'd be more time consuming.

So my questions are:

1. Is this even an issue? And if so, does it depend at all on the size of the crack relative to size of panel, for example a 2inch strip where the fracture extends half way through?
2. Short of replacing it is there anything else I should do or do do differently, for example caulk or just mudding over it?
3. Somewhat tangential, but if you needed to replace a 3inch strip at the end of a panel, would it be better practice to just replace the whole panel, or to try and use a drywall saw and only replaced the damaged strip at the edge?

Answer 1

Not an issue.

Someone just hit the nail too hard when driving it in.

I think most seams/edges will have that damage at a couple of nails/screws, drywall is not that crack resistant, it is more for a flat surface to put paint on(fire resistance also). It is the paper surface that holds it together.

Could mud it over, but most people will not be bother.